Equipment Grant: Symbolic Computing Equipment for NonlinearPlasma and Semiconductor Research

这项研究设备补助金将使购买麦金塔电脑 IIci计算机和程序Mathematica作为必要的助手， 主要研究者的研究活动。 的研究项目 涵盖了不同的主题，这些主题有两个共同的属性： 带电粒子的集体运动，主要是在等离子体中， 非线性过程 这项研究是理论性的， 分析和数值方法，其中符号计算将 在分析部分越来越重要。 调查 离子束，用于中性束加热和溅射，试图 导出离子分布函数的解析表达式， 电场、电势等，并带有被测射束的模型 密度为起点。 寻找更现实、更稳定的 分配功能是可能的。 解析表达式 碰撞半导体中的载流子速度在 可能空间周期性空间电荷及其器件的研究 应用. 非线性Vlasov-Maxwell方程组的研究 对可积系统的研究将成为对 关于随时间变化的电场的混沌行为。 混沌 对于半导体中的载流子速度也存在解决方案。 在 所有项目的非线性解决方案发现，利用李群对称性 的微分方程给出了结果，要么不知道以前 或者更有效率地被发现。

This Research Equipment Grant will enable acquisition of a Macintosh IIci computer and the program Mathematica as essential aides in the Principal Investigator's research activities. The research projects encompass diverse topics which share two common attributes: the collective motion of charged particles, chiefly in plasmas, and nonlinear processes. The research is theoretical with a mixture of analytical and numerical approaches where symbolic computation will be increasingly important in the analytical portions. The investigation of ion beams, used in neutral beam heating and sputtering, attempts to derive analytical expressions for the ion distribution functions, the electric fields, potentials, etc. with a model for the measured beam density as the starting point. Finding more realistic and stable distribution functions is possible. Analytical expressions for the carrier speed in collisional semiconductors are useful in the investigation of possible spatially periodic space charge and device applications. The research of the nonlinear Vlasov-Maxwell equations on integrable systems will become an investigation of the boundaries of chaotic behavior for time-dependent electric fields. Chaotic solutions may exist for the carrier speed in semiconductors also. In all projects nonlinear solutions found by using Lie group symmetries of differential equations have given results either not known before or found much more efficiently.